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A ray of light travelling in water is incident on a glass plate immersed in it. When the angle of incidence is 51° the reflected ray is totally plane polarised. Find the refractive index of the glass. (Refractive index of water =1.3 and tan 51°=1.235)

Asked in GUJCET 2008 · Brewster's law and polarisation by reflection

• (1) 1.605
• (2) 1.305
• (3) 1.33
• (4) 1.805

Step-by-step solution

Why the other options are wrong

• (2) 1.305 is little more than the index of the water itself. No step of Brewster's law produces it: the tangent gives the ratio of the two indices, so μ_g=1.3×1.235=1.605.
• (3) 1.33 is the index of water quoted from memory. The question asks for the glass, and μ_g=μ_w tan iₚ=1.605.
• (4) No slip gives 1.805: it would need tan iₚ=(1.805)/(1.3)=1.389, a polarising angle of about 54° and not the 51° printed.

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